Palm Springs International Airport (PSP) is about 10 minutes from downtown Palm Springs. Definitely the most convenient airport to fly into- although no direct flights from St. Louis.
Ontario International Airport (ONT) is about an hour and 15 minute drive from PS (75 miles away).
John Wayne Airport- Santa Ana (SNA) is about an hour and 30 minute drive from PS depending on traffic (105 miles away).
Los Angeles International Airport (LAX) is roughly a 2 hour and 30 minute drive to PS depending on traffic (125 miles away).